Question

How correct is the statement $\int_1^∞ (\frac{1}{x^2}) \,dx= 1$?

score 115 · Answer 1 · 2022-10-21 14:52:47

115

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How correct is the statement $\int_1^∞ (\frac{1}{x^2}) \,dx= 1$?

Published on 21 Oct 2022 - 14:52

score 233 · Answer 2 · 2022-10-24 20:08:08

233

Views

Can Rudin's PMA Theorem 6.17 be proven by using Riemann (as opposed to Darboux) integrals?

Published on 24 Oct 2022 - 20:08

score 50 · Answer 3 · 2022-10-26 10:20:46

Convergence of $ z_n=\frac{1}{n} \left[ x_1\left(1+\frac{x}{n}\right)^n + x_2\left(1+\frac{x}{n-1}\right)^{n-1} + \dots + x_n(1+x) \right] $

score 68 · Answer 4 · 2026-03-30 04:21:11

68

Views

Why isn't Riemann sum infinitesimal in nonstandard analysis?

Published on 30 Mar 2026 - 4:21

score 73 · Answer 5 · 2022-11-06 20:36:48

73

Views

If $f$ is integrable in $[a,b]\rightarrow\mathbb R$ and $f(x)≥0$ except for a value $c$ such that $f(c)=-1$. Show that the integral of is positive.

Published on 06 Nov 2022 - 20:36

score 147 · Answer 6 · 2022-11-07 22:22:51

147

Views

Simple Riemann Integrability Question

Published on 07 Nov 2022 - 22:22

score 55 · Answer 7 · 2022-11-08 22:40:40

55

Views

Why are cutpoints in Riemann integration defined to be less than or equal to eachother?

Published on 08 Nov 2022 - 22:40

score 82 · Answer 8 · 2026-02-23 13:40:33

82

Views

Riemann Sums Approximation

Published on 23 Feb 2026 - 13:40

score 98 · Answer 9 · 2022-11-12 13:27:28

98

Views

Is my proof correct for $|f(x)-f(y)|\leq k|g(x)-g(y)|^c, f,g:[a,b]\to R,\text{ and }g\text{ is Riemann integrable}\Rightarrow f \text{ integrable}$

Published on 12 Nov 2022 - 13:27

score 61 · Answer 10 · 2026-04-02 03:53:35

61

Views

Question about convergence of Riemann Sums

Published on 02 Apr 2026 - 3:53

score 112 · Answer 11 · 2022-11-16 09:01:45

112

Views

If $f$ is Riemann int. on $[0,b)$ for all $b>0$ and Lebesgue int. on $[0,\infty)$ then $\int_{[0,\infty)}f\,dm = \lim_{b\to\infty}\int_0^bf(x)\,dx$

Published on 16 Nov 2022 - 9:01

score 43 · Answer 12 · 2026-04-05 19:02:29

43

Views

Riemann sum of a periodic function

Published on 05 Apr 2026 - 19:02

score 52 · Answer 13 · 2022-11-17 15:08:27

52

Views

Estimates for the difference between Riemann lower/upper sum and the integration

Published on 17 Nov 2022 - 15:08

score 74 · Answer 14 · 2026-03-25 22:25:13

74

Views

Set of step function is dense in piecewise functions set, understanding of the statement.

Published on 25 Mar 2026 - 22:25

score 40 · Answer 15 · 2026-04-01 10:30:50

40

Views

If $\frac1n\sum_{i=1}^n1_{[0,\:a)}(x_i)\to a$ for all $a$, can we conclude $\frac1n\sum_{i=1}^nf(x_i)\to\int_{[0,\:1)}f$

Published on 01 Apr 2026 - 10:30

List Question

How correct is the statement $\int_1^∞ (\frac{1}{x^2}) \,dx= 1$?

Can Rudin's PMA Theorem 6.17 be proven by using Riemann (as opposed to Darboux) integrals?

Convergence of $ z_n=\frac{1}{n} \left[ x_1\left(1+\frac{x}{n}\right)^n + x_2\left(1+\frac{x}{n-1}\right)^{n-1} + \dots + x_n(1+x) \right] $

Why isn't Riemann sum infinitesimal in nonstandard analysis?

If $f$ is integrable in $[a,b]\rightarrow\mathbb R$ and $f(x)≥0$ except for a value $c$ such that $f(c)=-1$. Show that the integral of is positive.

Simple Riemann Integrability Question

Why are cutpoints in Riemann integration defined to be less than or equal to eachother?

Riemann Sums Approximation

Is my proof correct for $|f(x)-f(y)|\leq k|g(x)-g(y)|^c, f,g:[a,b]\to R,\text{ and }g\text{ is Riemann integrable}\Rightarrow f \text{ integrable}$

Question about convergence of Riemann Sums

If $f$ is Riemann int. on $[0,b)$ for all $b>0$ and Lebesgue int. on $[0,\infty)$ then $\int_{[0,\infty)}f\,dm = \lim_{b\to\infty}\int_0^bf(x)\,dx$

Riemann sum of a periodic function

Estimates for the difference between Riemann lower/upper sum and the integration

Set of step function is dense in piecewise functions set, understanding of the statement.

If $\frac1n\sum_{i=1}^n1_{[0,\:a)}(x_i)\to a$ for all $a$, can we conclude $\frac1n\sum_{i=1}^nf(x_i)\to\int_{[0,\:1)}f$

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